Ratios and Graphs of Trigonometric Functions · Form 5
Ratios and Graphs of Trigonometric Functions: Common Mistakes
The mistakes that quietly cost marks in Ratios and Graphs of Trigonometric Functions, and how to avoid each one in the SPM exam.
In our experience teaching Ratios and Graphs of Trigonometric Functions, most lost marks come from a small set of repeated slips, not from a lack of understanding. Here they are, with the fix for each.
Mistakes to avoid
- Getting the sign wrong outside the first quadrant
- Sketching the wrong number of cycles for the given range
- Mislabelling the axes or the peak/trough values
Six more mistakes that quietly cost marks
- What students write: cos 240° ≈ 0.326 (calculator left in radian mode). → Why it loses marks: that value is the cosine of 240 radians, not 240°, so every later step is wrong. → Correct working: set the calculator to DEG; cos 240° = −0.5.
- What students write: sin x = 1/√2 so x = 45° only. → Why it loses marks: the reference angle is not the whole answer; the second-quadrant solution is dropped. → Correct working: sine is positive in Q1 and Q2, so x = 45° and x = 135°.
- What students write: for sin 2x = 1/2, 0° ≤ x ≤ 360°, only x = 15° and 75°. → Why it loses marks: with 2x the range becomes 0° ≤ 2x ≤ 720°, so there are four solutions, not two. → Correct working: 2x = 30°, 150°, 390°, 510°, giving x = 15°, 75°, 195°, 255°.
- What students write: sin x² for the square of sin x. → Why it loses marks: sin x² means the sine of (x²), a different quantity, so the marker cannot award the step. → Correct working: write (sin x)² as sin²x.
- What students write: tan 90° = 1 (or an invented number). → Why it loses marks: tangent is undefined at 90° and 270° (cosine is zero), so no value can be given. → Correct working: state that tan 90° is undefined; the graph has an asymptote there.
- What students write: reading a peak as y = 2 because it sits two squares above the axis. → Why it loses marks: if each square is 0.5 unit the peak is y = 1, so the amplitude is misread. → Correct working: check the axis scale first; two squares × 0.5 = 1, so the maximum is y = 1.
A quick self-check before you submit
Before you submit, run three fast checks on any trig answer: is the calculator in degree mode, does each solution actually lie inside the stated range, and does the sign of every value match the quadrant it came from? Ten seconds of checking recovers the marks these six slips quietly remove.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Why does my answer change when I switch the calculator between DEG and RAD?
Because the calculator is measuring the angle in different units. In DEG mode 240 means 240 degrees; in RAD mode it means 240 radians, a completely different angle.
SPM trigonometry works in degrees, so set the calculator to DEG before any question and check the small D or R indicator on the screen.
For sin 2x = …, why do I suddenly get four answers instead of two?
Because the doubled angle sees a doubled range. If 0° ≤ x ≤ 360° then 0° ≤ 2x ≤ 720°, so 2x can land on the required value up to four times before you halve it back to x.
Always widen the range for the multiple angle first, list every value, then divide.
Is sin²x the same as sin x²?
No. sin²x is standard shorthand for (sin x)², the sine taken first and then squared.
Writing sin x² instead means the sine of x², which squares the angle first, a different quantity. Keep the square on the whole ratio: (sin x)² = sin²x.
Markers read the two notations literally.